Deputy White House counsel Jay B. Stephens was named yesterday by Attorney General Edwin Meese III to be interim U.S. attorney for the District of Columbia, and Meese said he would recommend Stephens as the permanent replacement for Joseph E. diGenova, who left to join a private law firm.

The selection, which sources said was made over the weekend, came as a surprise to many observers because Stephens, mentioned early as a possible contender for the job, had said as recently as last week that he was not interested in leaving his White House post.

Coincidentally, Stephens' White House job involved helping to select persons to be named as judges and U.S. attorneys. Stephens, 41, who was on vacation yesterday and could not be reached for comment, also helped Reagan administration officials prepare to testify in the perjury trial of former White House aide Michael K. Deaver.

People knowledgeable about the selection process said the appointment of Stephens, who has spent seven years in the Justice Department and the White House, signals the Reagan administration's commitment to continue the highly publicized public corruption and drug investigations undertaken by diGenova. But other sources said Stephens may lack aggressiveness and thoroughness, based on an incident involving Lt. Col. Oliver L. North's shredding of documents early in the Iran-contra probe. According to testimony during the Iran-contra hearings, it was Stephens who called Fawn Hall, who then was North's secretary, on Thanksgiving 1986 to inquire about a published report that North had shredded crucial documents.

Hall testified during the hearings that she told Stephens "we shred every day," and that he did not press for additional information. The White House then denied the press report.

DiGenova, who has been criticized for leaving as U.S. attorney while several investigations of Mayor Marion Barry's administration are incomplete, said in an interview yesterday that Stephens "as an alumnus of this office and the Department of Justice . . . is an excellent choice to lead this office and continue its important work."

Other prosecutors said that because of the posts Stephens held in the Justice Department and in the White House, he is familiar with the continuing investigations and many of the problems facing this U.S. attorney's office.

"There should be no major break in the investigations," a former prosecutor said yesterday.

Under a 1986 law, the attorney general has the authority to appoint an interim U.S. attorney for 120 days pending confirmation of a presidential nominee. A spokesman for the Senate Judiciary Committee said confirmation for most U.S. attorneys usually takes from six to eight weeks after a nomination is made.

"The amount of time depends somewhat on whether there is a controversy over the appointment," the spokesman said.

Some sources questioned whether the Democrat-controlled Senate would confirm any Reagan nominee for the post as the District's top law enforcement official. The U.S. attorney's office here is the largest in the country and the only one to have responsibility for prosecuting both local and federal crimes.

Although an appointment as U.S. attorney is for a four-year term, top federal prosecutors serve at the pleasure of the president. Because of the upcoming presidential election, any new U.S. attorney here is not expected to serve more than 18 months, several sources said.

Stephens, an Iowa native and a graduate of Harvard University and Harvard Law School who also studied at New College, Oxford, came to Washington in 1973 to work as an associate at Wilmer, Cutler & Pickering. He joined the Watergate prosecutor's office in 1975, then left to be associate general counsel at the Overseas Private Investment Corp.

He joined the U.S. attorney's office here in 1977, working as a prosecutor in D.C. Superior Court. His most celebrated work there was as a prosecutor in the murder trial of Bernard C. Welch for the shooting death of Dr. Michael Halberstam.

In 1981, Stephens joined the Justice Department as special counsel to D. Lowell Jensen, who was then head of the department's criminal division. As Jensen, now a U.S. district judge in California, rose through the department's ranks, first to associate attorney general and then to deputy attorney general, Stephens moved with him.

Stephens joined the White House staff as deputy counsel in April 1986.

Jensen, now a federal judge and formerly Stephens' boss at Justice, said, "I think this is a very fine appointment. I think he is a true professional and I think that he will be an outstanding U.S. attorney for the District."

Jensen said Stephens had "proven himself as a trial lawyer, and from what I know of him he is going to prove himself as a very fine leader and administrator."

Former U.S. attorney Charles F.C. Ruff said Stephens would be an "absolutely first-rate U.S. attorney." Ruff, who worked with Stephens in the Watergate prosecutor's office and supervised him at the U.S. attorney's office, said Stephens is "recognized by everyone as top-notch."

DiGenova had lobbied the White House to pick diGenova's principal assistant, Timothy J. Reardon III, as his replacement. Reardon, whose father was a special assistant to President Kennedy, was backed by officials of the U.S. Park Police, U.S. Capitol Police and the D.C. Black Police Caucus.

But Reardon was opposed by many prosecutors in the U.S. attorney's office, who complained that he had served more as a personal aide to diGenova instead of the office's top supervisor.

Reardon is the acting U.S. attorney until Stephens returns from vacation and assumes the post, probably on Monday.